This study proposes the stochastic inventory mathematical model for the continuous review inventory systems under simultaneously taking account to the controllable lead time and time value of money. In the model, the shortages are allowed and the total amount of stockout during the stockout period is considered to be a mixture of backorders and lost sales. In this paper, we consider the case of the lead time demand follows a normal distribution, and then use the DCF approach procedure to solve the optimal solution. We also develop an algorithm to obtain the optimal ordering strategy for each case (the lead time demand follows normal distribution or distribution free). Furthermore, for all models proposed in this paper, the effects of parameters are also included.